When Joseph R. Biden Jr. visited San Francisco as a freshly minted senator and single father in the early 1970s, it was a well-known local fund-raiser and stay-at-home mother of five, Nancy Pelosi, who lent him her Jeep Wrangler to get around town.

Over the next five decades, the two old-school Catholic Democrats who grew up in the era of Elvis Presley and were inspired by the election of the country’s first Catholic president, John F. Kennedy, cultivated a natural friendship.

They discovered that they both carried rosaries in their pockets. They learned how to wield power in Washington as leaders of top-tier congressional committees: the House Intelligence and Appropriations Committees for her, the Senate Foreign Relations and Judiciary Committees for him.

In May, at the twilights of their long careers, Mr. Biden, 81, awarded Ms. Pelosi, 84, the Presidential Medal of Freedom, anointing her the “greatest speaker of the House of Representatives in history.”

That was then. In July, Ms. Pelosi began pushing for Mr. Biden to exit the presidential race, and the two have not spoken since he made the difficult decision to step aside. There are multiple reports that Mr. Biden is angry with her. (On Wednesday, a person close to him said he was “unhappy” with the way things went.)

Ms. Pelosi has been making the rounds on a book tour, which has given her the opportunity to disparage Mr. Biden’s political team for failing, she has said, to put in place a winning presidential campaign.